{"id":11401,"date":"2022-03-19T03:26:12","date_gmt":"2022-03-19T01:26:12","guid":{"rendered":"http:\/\/journals.khnu.km.ua\/vestnik\/?p=11401"},"modified":"2022-04-14T11:07:18","modified_gmt":"2022-04-14T08:07:18","slug":"modelyuvannya-kiberfizychnoyi-imunosensornoyi-systemy-na-pryamokutnij-reshitczi-z-vykorystannyam-riznyczevyh-rivnyan-iz-zapiznennyam","status":"publish","type":"post","link":"https:\/\/journals.khnu.km.ua\/vestnik\/?p=11401","title":{"rendered":"\u041c\u043e\u0434\u0435\u043b\u044e\u0432\u0430\u043d\u043d\u044f \u043a\u0456\u0431\u0435\u0440\u0444\u0456\u0437\u0438\u0447\u043d\u043e\u0457 \u0456\u043c\u0443\u043d\u043e\u0441\u0435\u043d\u0441\u043e\u0440\u043d\u043e\u0457 \u0441\u0438\u0441\u0442\u0435\u043c\u0438 \u043d\u0430 \u043f\u0440\u044f\u043c\u043e\u043a\u0443\u0442\u043d\u0456\u0439 \u0440\u0435\u0448\u0456\u0442\u0446\u0456 \u0437 \u0432\u0438\u043a\u043e\u0440\u0438\u0441\u0442\u0430\u043d\u043d\u044f\u043c \u0440\u0456\u0437\u043d\u0438\u0446\u0435\u0432\u0438\u0445 \u0440\u0456\u0432\u043d\u044f\u043d\u044c \u0456\u0437 \u0437\u0430\u043f\u0456\u0437\u043d\u0435\u043d\u043d\u044f\u043c"},"content":{"rendered":"

<\/p>\n

\u041c\u041e\u0414\u0415\u041b\u042e\u0412\u0410\u041d\u041d\u042f \u041a\u0406\u0411\u0415\u0420\u0424\u0406\u0417\u0418\u0427\u041d\u041e\u0407 \u0406\u041c\u0423\u041d\u041e\u0421\u0415\u041d\u0421\u041e\u0420\u041d\u041e\u0407 \u0421\u0418\u0421\u0422\u0415\u041c\u0418 \u041d\u0410 \u041f\u0420\u042f\u041c\u041e\u041a\u0423\u0422\u041d\u0406\u0419 \u0420\u0415\u0428\u0406\u0422\u0426\u0406 \u0417 \u0412\u0418\u041a\u041e\u0420\u0418\u0421\u0422\u0410\u041d\u041d\u042f\u041c \u0420\u0406\u0417\u041d\u0418\u0426\u0415\u0412\u0418\u0425 \u0420\u0406\u0412\u041d\u042f\u041d\u042c \u0406\u0417 \u0417\u0410\u041f\u0406\u0417\u041d\u0415\u041d\u041d\u042f\u041c<\/p>\n

MODELING OF THE CYBER-PHYSICAl IMMUNOSENSOR SYSTEM IN THE RECTANGULAR LATTICE BY USING DIFFERENCE EQUATIONS WITH DELAY<\/p>\n

\u00a0<\/strong>\u0421\u0442\u043e\u0440\u0456\u043d\u043a\u0438: 41-48. \u041d\u043e\u043c\u0435\u0440: \u21166, 2021 (303)<\/strong> \"\"<\/a>
\n\u0410\u0432\u0442\u043e\u0440\u0438<\/strong>:
\n\u0421\u0412\u0415\u0420\u0421\u0422\u042e\u041a \u0410. \u0421
\n\u0422\u0435\u0440\u043d\u043e\u043f\u0456\u043b\u044c\u0441\u044c\u043a\u0438\u0439\u00a0 \u043d\u0430\u0446\u0456\u043e\u043d\u0430\u043b\u044c\u043d\u0438\u0439 \u043c\u0435\u0434\u0438\u0447\u043d\u0438\u0439 \u0443\u043d\u0456\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442 \u0456\u043c\u0435\u043d\u0456 \u0406. \u042f. \u0413\u043e\u0440\u0431\u0430\u0447\u0435\u0432\u0441\u044c\u043a\u043e\u0433\u043e
\nORCID ID: 0000-0001-8644-0776
\ne-mail: sverstyuk@tdmu.edu.ua
\n\u0417\u0410\u0413\u041e\u0420\u041e\u0414\u041d\u0410 \u041d. \u0412.
\n\u0422\u0435\u0440\u043d\u043e\u043f\u0456\u043b\u044c\u0441\u044c\u043a\u0438\u0439 \u043d\u0430\u0446\u0456\u043e\u043d\u0430\u043b\u044c\u043d\u0438\u0439 \u0442\u0435\u0445\u043d\u0456\u0447\u043d\u0438\u0439 \u0443\u043d\u0456\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442 \u0456\u043c\u0435\u043d\u0456\u00a0 \u0406. \u041f\u0443\u043b\u044e\u044f
\nORCID ID: 0000-0002-1808-835X
\ne-mail: zagorodna.n@gmail.com
\n\u041c\u0410\u0420\u0426\u0415\u041d\u042e\u041a \u0412. \u041f.
\n\u0423\u043d\u0456\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442 \u0432 \u0411\u0435\u043b\u044c\u0441\u044c\u043a\u043e \u0411\u044f\u043b\u0430, \u041f\u043e\u043b\u044c\u0449\u0430
\nORCID ID: 0000-0001-5622-1038
\ne-mail: vmartsenyuk@ath.bielsko.pl
\n\u0421\u0422\u0410\u0414\u041d\u0418\u041a \u041c. \u0410.
\n\u0422\u0435\u0440\u043d\u043e\u043f\u0456\u043b\u044c\u0441\u044c\u043a\u0438\u0439 \u043d\u0430\u0446\u0456\u043e\u043d\u0430\u043b\u044c\u043d\u0438\u0439 \u0442\u0435\u0445\u043d\u0456\u0447\u043d\u0438\u0439 \u0443\u043d\u0456\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442 \u0456\u043c\u0435\u043d\u0456\u00a0 \u0406. \u041f\u0443\u043b\u044e\u044f
\nORCID ID: 0000-0002-0287-2254
\ne-mail: maria.stadnyk@gmail.com
\n\u0421\u0412\u0415\u0420\u0421\u0422\u042e\u041a \u0421. \u0410.
\n\u0422\u0435\u0440\u043d\u043e\u043f\u0456\u043b\u044c\u0441\u044c\u043a\u0438\u0439\u00a0 \u043d\u0430\u0446\u0456\u043e\u043d\u0430\u043b\u044c\u043d\u0438\u0439 \u043f\u0435\u0434\u0430\u0433\u043e\u0433\u0456\u0447\u043d\u0438\u0439 \u0443\u043d\u0456\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442 \u0456\u043c\u0435\u043d\u0456 \u0412\u043e\u043b\u043e\u0434\u0438\u043c\u0438\u0440\u0430 \u0413\u043d\u0430\u0442\u044e\u043a\u0430
\nORCID ID: 0000-0001-5595-4918
\ne-mail: sverstiuks<\/u>@<\/u>gmail<\/u>.<\/u>com<\/u>
\n\u0410ndriy SVERSTYUK
\nTernopil National Medical University. J. Gorbachevsky
\nNATALIYA\u00a0ZAGORODNA
\nTernopil National Technical University named after Puliy
\nVASYL MARTSENYUK
\nUniversity of Bielsko-Bia\u0142a, Poland
\nMARIA STADNIK
\nTernopil National Technical University named after Puliy
\nSOFIA SVERSTYUK
\nTernopil National Pedagogical University named after Volodymyr Hnatiuk
\nDOI:<\/strong> https:\/\/www.doi.org\/10.31891\/2307-5732-2021-303-6-41-48<\/a>
\n\u0420\u0435\u0446\u0435\u043d\u0437\u0456\u044f\/Peer review : <\/strong>04.11.2021 \u0440.
\n\u041d\u0430\u0434\u0440\u0443\u043a\u043e\u0432\u0430\u043d\u0430<\/strong>\/<\/strong>Printed<\/strong> :<\/strong> 30.12.2021 \u0440.<\/p>\n

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\n\u041a\u043b\u044e\u0447\u043e\u0432\u0456 \u0441\u043b\u043e\u0432\u0430:<\/strong> \u043a\u043e\u043c\u043f\u2019\u044e\u0442\u0435\u0440\u043d\u0435 \u043c\u043e\u0434\u0435\u043b\u044e\u0432\u0430\u043d\u043d\u044f, \u043a\u0456\u0431\u0435\u0440\u0444\u0456\u0437\u0438\u0447\u043d\u0430 \u0441\u0438\u0441\u0442\u0435\u043c\u0430, \u0456\u043c\u0443\u043d\u043e\u0441\u0435\u043d\u0441\u043e\u0440\u043d\u0430 \u0441\u0438\u0441\u0442\u0435\u043c\u0430, \u0440\u0456\u0437\u043d\u0435\u0446\u0435\u0432\u0456 \u0440\u0456\u0432\u043d\u044f\u043d\u043d\u044f \u0456\u0437 \u0437\u0430\u043f\u0456\u0437\u043d\u0435\u043d\u043d\u044f\u043c, \u043f\u0440\u044f\u043c\u043e\u043a\u0443\u0442\u043d\u0430 \u0440\u0435\u0448\u0456\u0442\u043a\u0430.<\/p>\n

\u0420\u043e\u0437\u0448\u0438\u0440\u0435\u043d\u0430 \u0430\u043d\u043e\u0442\u0430\u0446\u0456\u044f \u0430\u043d\u0433\u043b\u0456\u0439\u0441\u044c\u043a\u043e\u044e \u043c\u043e\u0432\u043e\u044e<\/strong><\/p>\n

Due to the rapid development of science and technology, there is a growing need for accurate measurement of indicators that reflect and characterize the various physical processes in the alimentary and defense industry, economy, health, environmental changes and in other areas of human existence. Accordingly, this leads to the popularization of cyberphysical systems, which are characterized by a close connection between the studied physical object and the relevant software. Such attention to cyberphysical systems is the basis for the problem of developing new mathematical and computational tools for obtaining and analyzing the results of numerical modelling in their design. The main purpose of the article is to develop a mathematical and computer model of the cyberphysical immunosensory system using difference equations with delay on a rectangular lattice and investigate it stability. The methodological tools of the study are the difference equations with the delay. The object of research is the process of modelling the cyberphysical immunosensory system. The construction of the model in the article is carried out in the following logical sequence: the study of the functional diagram of the cyberphysical system, determining the requirements for the mathematical model, computer modelling of the investigated model. The results of experimental studies are received in the form of lattice images of antigens, antibodies, lattice images of the probability of binding of antigens to antibodies in biopixels, images of fluorescent pixels of systems and electrical signal from the converter, which characterizes the number of fluorescent pixels.<\/p>\n

Keywords:<\/strong> computer simulation, cyberphysical system, immunosensory system, difference equations with delay \u2013 rectangular grid.<\/p>\n

References<\/strong><\/p>\n

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